Question

Formulate the following problem as a linear programming problem and solve it using the graphical method of corners.

A company produces two types of similar products, product A and product B. Product A requires 2 hours to produce and product B requires 4 hours to produce. The company has only 800 hours to use in production each day and can only produce up to 300 of both products per day. If the company sells product A for $22.50 and product B for $45.00, how many of each type should be produced each day to maximize sales revenue?
a) A: 200, B: 100
b) A: 250, B: 50
c) A: 150, B: 150
d) A: 100, B: 200

Answer 1

The company should produce A: 200, B: 100 each day to maximize sales revenue

Formulating the following as a linear programming

From the question, we have the following parameters that can be used in our computation:

Products = A and B

The company sells product A for $22.50 and product B for $45.00

So, the objective function is

Max Z = 22.5A + 45B

Then we have the constraints to be

• Total production time cannot exceed 800 hours: 2A + 4B ≤ 800
• Total production cannot exceed 300 units: A + B ≤ 300
• Non-negativity constraints: A ≥ 0, B ≥ 0

Solving graphically, we have the feasible points to be

(A, B) = (200, 100)

Hence, the company should produce A: 200, B: 100 each day to maximize sales revenue